Generalized Ramsey Numbers: Forbidding Paths with Few Colors
نویسندگان
چکیده
منابع مشابه
Tripartite Ramsey numbers for paths
In this article, we study the tripartite Ramsey numbers of paths. We show that in any two-coloring of the edges of the complete tripartite graph K(n, n, n) there is a monochromatic path of length (1− o(1))2n. Since R(P2n+1,P2n+1) = 3n, this means that the length of the longest monochromatic path is about the same when two-colorings of K3n and K(n, n, n) are considered. © 2007 Wiley Periodicals,...
متن کاملOn generalized Ramsey numbers
Let f1 and f2 be graph parameters. The Ramsey number r(f1 ≥ m; f2 ≥ n) is defined as the minimum integer N such that any graph G on N vertices, either f1(G) ≥ m or f2(G) ≥ n. A general existence condition is given and a general upper bound is shown in this paper. In addition, suppose the number of triangles in G is denoted by t(G). We verify that (1− o(1))(24n) ≤ r(t ≥ n; t ≥ n) ≤ (1 + o(1))(48...
متن کاملGeneralized Ramsey Theory for Multiple Colors
In this paper, we study the generalized Ramsey number r(G, , . . ., Gk) where the graphs GI , . . ., Gk consist of complete graphs, complete bipartite graphs, paths, and cycles. Our main theorem gives the Ramsey number for the case where G 2 , . . ., G,, are fixed and G, ~_C, or P,, with n sufficiently large . If among G2 , . . ., G k there are both complete graphs and odd cycles, the main theo...
متن کاملRamsey Numbers of Squares of Paths
The Ramsey number R(G,H) has been actively studied for the past 40 years, and it was determined for a large family of pairs (G,H) of graphs. The Ramsey number of paths was determined very early on, but surprisingly very little is known about the Ramsey number for the powers of paths. The r-th power P r n of a path on n vertices is obtained by joining any two vertices with distance at most r. We...
متن کاملThree-Color Ramsey Numbers For Paths
We prove for sufficiently large n the following conjecture of Faudree and Schelp : R(Pn, Pn, Pn) = { 2n− 1 for odd n, 2n− 2 for even n, for the three-color Ramsey numbers of paths on n vertices. ∗2000 Mathematics Subject Classification: 05C55, 05C38. The second author was supported in part by OTKA Grants T038198 and T046234.
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: The Electronic Journal of Combinatorics
سال: 2020
ISSN: 1077-8926
DOI: 10.37236/8801